SPECTRAL GAP OF THE DISCRETE LAPLACIAN ON TRIANGULATIONS

Trou spectral du Laplacien discret des triangulations

Yassin Chebbi (1, 2)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 LR/18ES15 - Université de Monastir

Our goal in this paper is to find an estimate for the spectral gap of the Laplacian on a 2-simplicial complex consisting on a triangulation of a complete graph. An upper estimate is given by generalizing the Cheeger constant. The lower estimate is obtained from the first non-zero eigenvalue of the discrete Laplacian acting on the functions of certain sub-graphs.

Domaines: Théorie spectrale [math.SP]

Yassin Chebbi. SPECTRAL GAP OF THE DISCRETE LAPLACIAN ON TRIANGULATIONS. Journal of Mathematical Physics, 2020. ⟨hal-02162835⟩